The operation to dismantle the tents pitched in a cramped space along the Grand Canal began shortly after 7.00 a.m. on Thursday.
Workers sprayed numbers on around 80 tents before the operation commenced.
The Irish government has said it is not currently in a position to provide accommodation to all male asylum seekers arriving in the country.
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The latest figures showed there were 1,939 applicants awaiting an offer of accommodation.
Contractors began erecting additional barriers around the site from 5.00 a.m. on Thursday.
More than 90 minutes passed before the international-protection applicants were informed by volunteers they were being asked to move.
The volunteers assisted with uncovering tarps from the tents as they made efforts to ensure the applicants were awake and packed before the operation began.
Police officers, or Gardaí, began to arrive at the scene from 6.45 a.m.
The men started boarding multiple coaches to be transferred to other sites at 7.00 a.m.
This is the fifth time asylum seekers sleeping in tents have been moved from parts of Dublin city in recent months, twice at the International Protection Office on Mount Street and three times along the Grand Canal.
Hundreds of applicants have been offered state-provided shelter through the operations.
The Irish government is operating state-provided shelter at multiple sites where it says it has robust, weather-proof tents.
It has said the sites also have toilets and showers, health services, indoor areas where food is provided and facilities to charge phones.
Personal devices, access to transport to and from Dublin City Centre, and 24-hour onsite security were provided.
One young man who was offered state-provided accommodation on Thursday said he was fleeing conflict in Somalia.
He added that he had been awaiting an offer of accommodation in Ireland since February.
Speaking to the PA news agency, he said that men at the camp were fleeing conflict.
He also said he believed the move to state-provided shelter was good as there was no access to facilities at the makeshift camp.
He further expressed concern about “misinformation and propaganda” being spread about the men online and in the media.